As is known, repeat-pass satellite Synthetic Aperture Radar (SAR) interferometry is a very effective technology for measuring terrain displacements due to subsidence, landslides, earthquakes and volcanic phenomena, as reviewed in P. A. Rosen, S. Hensley, I. R. Joughin, F. K. Li, S. N. Madsen, E. Rodriguez, R. M. Goldstein, Synthetic Aperture Radar interferometry, Proceedings of the IEEE, vol. 88, no. 3, pp. 333-382, March 2000, and in R. Bamler, P. Hartl, Topical Review: Synthetic Aperture Radar interferometry, Inverse Problems, vol. 14, pp. R1-R54, 1998.
In particular, the repeat-pass satellite SAR interferometry is based on a coherent sensing of the Earth's surface through satellite-mounted (or aeroplane-mounted or ground-based) radars which image the Earth's surface with a spatial resolution of the order of one meter or few meters with current spaceborne sensors (less for airborne or ground-based radars). A combination of backscattering signals from all sources within each resolution cell results in an amplitude and a phase associated with the resolution cell or pixel in the SAR image.
In detail, the phase of a single pixel in a SAR image, which is associated with the portion of terrain within the resolution cell, can be modeled as the sum of four contributions:                a first contribution φs is a phase associated with the scattering mechanism in the given resolution cell;        a second contribution φr is related to the distance r between the sensor and the resolution cell, and to the wavelength λ of the sensor, the second contribution φr being defined as φr=4πr/λ;        a third contribution φa is a phase associated with the delay introduced by the atmosphere; and        a fourth contribution φn is a residual from the model, including phase noise.        
Taking into account, in first instance, only the scattering-related phase contribution φs and the sensor-resolution cell distance phase contribution φr, if two SAR images are acquired at different times and with slightly different look angles, and under the hypothesis that the scattering behaviour of the resolution cell is identical in the two acquisitions, the phase difference of the two co-registered images, the so-called “interferometric phase”, depends on the elevation of the resolution cell and on its displacements, since the term φs due to the scatterer is removed in the difference. A Digital Elevation Model (DEM) can be used to determine and remove the contribution of the terrain elevation from the interferometric phase and, therefore, to obtain terrain displacements.
In principle, differential interferometry can measure terrain displacements of few millimeters. However, the accuracy and the feasibility of the measurements are influenced by different error sources, that can be divided in two groups: noise, mainly due to decorrelation between the SAR images at different acquisitions, and systematic errors, due to limited accuracies of the orbital data and of the DEM used in the processing, and to different atmospheric conditions at the different acquisition dates.
In particular, decorrelation noise makes valid interferometric measurements possible only on a sparse set of points, called Persistent Scatterers (PS), which remain correlated at different acquisitions. PS typically correspond to resolution cells in which the dominant contribution to the signal comes from a single, point-like and stable during the time of the acquisitions, scattering mechanism. These scattering mechanisms are more frequent in the presence of buildings, infrastructures, rocks and bare soil.
Identification of the PS and then retrieval of their movement (together with their precise elevation) from a series of SAR acquisitions are key problems of Persistent Scatterer Interferometry (PSI).
A known method, named Permanent Scatterers method and disclosed in A. Ferretti, C. Prati, and F. Rocca, Permanent scatterers in SAR interferometry, IEEE Trans. Geosci. Remote Sensing, vol. 39, no. 1, pp. 8-20, January 2001, and in A. Ferretti, C. Prati, and F. Rocca, Non-linear subsidence rate estimation using permanent scatterers in differential SAR interferometry, IEEE Trans. Geosci. Remote Sensing, vol. 38, pp. 2202-2212, September 2000, with the idea of minimizing amplitude and phase dispersions in long series of full resolution SAR images, has introduced a new way of conceiving SAR interferometry.
In particular, the Permanent Scatterers method requires an identification of a preliminary set of PS, selected according to the stability in the different acquisitions of their signal amplitude (i.e., the modulus of the reflectivity). These points are analysed in relation with a phase model to determine the PS displacement velocity (assumed constant, the displacement evolves linearly with time) and elevation (or, more precisely, elevation correction with respect to the DEM used to flatten the phase), and to refine the PS selection.
These velocity and elevation contributions are then subtracted to the PS phase to determine the phase residuals, which contain atmospheric contribution, non-linear-with-time displacement, and the other non-modeled contributions including noise.
Atmospheric phase contribution can be then filtered out by exploiting its property of being spatially correlated (and temporally uncorrelated).
The atmospheric phase contributions calculated on the selected PS can then be used to estimate the atmospheric phase contributions in all points, by local or global (model-based) interpolations or fits.
These estimations can be subtracted from the relative images, which can be processed again to find better elevation and displacement velocity and new PS.
This procedure can be iterated several times to increase the number of PS found.
In this approach, it is fundamental to calibrate the data, both radiometrically and from the point of view of phase. In particular, radiometric calibration is necessary to analyze the signal amplitude dispersion, whereas calibrating the phase means removing orbital and atmospheric phase contributions, a step necessary not only for the analysis but also for the identification of all possible PS.